Dynamic assignment of a multi-skilled workforce in job shops: An approximate dynamic programming approach

We propose an approximate algorithm to dynamically assign a multi-skilled workforce to the stations of a job shop, with demand uncertainty and variability in the availability of the resources, to maximize productivity. Our proposed model is inspired by automotive glass manufacturing, where maximizing the surface area of manufactured safety glass during a given time frame is the key performance measure. We first develop the model of a traditional job shop with a set of stations, each with a particular number of machines, with distinct production performance levels, according to their utilization stage. Each product type needs to be processed on a subset of these stations according to a predefined sequence. Customers place their orders independently over time, specifying the units required of each product type. The inter-arrival of orders (demand) and processing times are assumed to be stochastic. We also suppose that the technicians have varied skill sets, according to which they can only work at a certain subgroup of stations, and variable availability depending on sick leave, vacations, etc. Hence, in order to maximize the predefined productivity index, the optimal assignment of technicians to the stations based on their skill sets and availability during each shift becomes a complex decision-making process. Given the stochastic and dynamic nature of this problem, we model the setting as a Markov Decision Process (MDP). Given its size, we propose to solve it using Approximate Dynamic Programming (ADP). We address the exponential growth of the action space by using a hill-climbing algorithm for action selection. To show the performance and effectiveness of the proposed algorithm, we use real company data and compare the results of the algorithm with the current policy in use, as well as other proposed policies. Applying our proposed method resulted in an average improvement of 15% in productivity compared to the best performing benchmark policy.